Pages

Tuesday, April 2, 2013

The universe as seen by Planck - Day one

I am currently attending the ESA run conference "The Universe as seen by Planck". I will be trying to write a summary each day of what I found interesting. To read about my motivation for this, please read yesterday's post. Below is the summary of the first day's talks. I apologise if the posts this week are overly technical. I don't have much time for writing these and this is the best I can do given the constraints. As always, if you don't understand, just ask questions in the comments.

Overall summary

Today was mostly about introducing the Planck experiment and its data. This is the first conference ESA has held since the data was released and in fact the first conference about Planck open to non-Planck scientists like myself at all. Therefore today was actually the first chance for the Planck collaboration to be honest about what their telescope has and has not been able to do. As a result, many of the talks that can lead to the most speculation will not come until tomorrow and Thursday. Still, there were some interesting things to come out of today. For example:

The reasons why no polarisation data from the CMB were used in likelihood analyses this time

(Not mentioned in a talk, but overheard from reliable sources) The reason no constraints on "\(g_\mathrm{NL}\)" were released this time

The existence of two "features" in the temperature power spectrum and many "features" in the temperature bispectrum

A few other curiosities

Here are, in no particular order, the things I found interesting today...

The missing data feature

People who watched the data release conference in March might have been a bit startled by the set of CMB maps that looked like the one below. I was. The particularly startling thing about these maps is the band slightly greyer in colour that persists right in the middle of the image and in the bottom left. The rest of the map looks quite similar to a typical map of the microwave radiation measured on the sky.

The red stuff is the galaxy. The blue/green stuff is the CMB. But what on Earth is that grey stripe? Talk about features!

Planck made quite a big deal about a number of "features" in their analysis (some of which I'll discuss below), but no mention was made of this feature that seems so obvious you can make it out by eye.

It turns out there is a well understood reason for this particular feature. Firstly, Planck had two independent telescopes on board. The low frequency instrument (LFI) and the high frequency instrument (HFI). These telescopes measured the intensity of microwave radiation at different sets of frequencies. This "feature" can only be seen in the LFI maps and is actually the result of those points on the sky being measured less often by LFI than all the others.

During one of LFI's sweeps of the sky it was hit by a cosmic ray. After this, it started taking measurements that were completely discrepant with expectations. How did LFI solve this? Just how you solve any other hardware problem. They turned it off and on again (apparently). Once back on, it was back to taking measurements that made sense. However, during all of this time, the telescope was sweeping across the sky, measuring different points on the sky. Every point that it missed during these events were therefore not measured in that sweep and remain measured one less time than the rest.

This grey band in the LFI maps is exactly that region of the sky. So, no excitement there.

Issues with polarisation

Planck hasn't just measured the temperature of the CMB, it has also measured the polarisation of the light in the CMB. If the big bang model is correct, then that polarisation should have certain statistical properties that reflect the sound waves in the primordial hydrogen, just like the temperature does.

In this release of data, none of the cosmological results from Planck have included any measurements of the polarisation. Why?

The answer to this question is that, at very large angular scales, the polarisation is not behaving well. Planck measures the temperature and polarisation at many different frequencies. The CMB should have exactly the same temperature and polarisation at every frequency. For the temperature, it does. For the polarisation, it doesn't seem to yet. So what's going on?

Well, the polarisation of the CMB is a very weak signal, much weaker than the temperature. Therefore, even though enough foreground radiation has been removed from the measured CMB to isolate the temperature signal accurately, this does not mean that the polarisation is not still contaminated.

The way that Planck can see most clearly that something is still a problem is by subtracting one map from another (i.e. two maps of the CMB temperature measured at different frequencies). If the polarisation is measured correctly then the remaining signal should be close to zero. If it isn't, there is a problem. One of the speakers showed a nice slide this morning (the slides aren't online and this isn't published so I can't show you the image) showing the amplitude of the polarisation signal in one of these subtracted maps as a function of angular scale. As the angles become small enough it definitely went to zero; however at the large angles it was still quite large.

In order to use the polarisation to obtain cosmological constraints Planck needs to understand all the angular scales correctly. Therefore, rather than work out what was going wrong, they decided to wait and solve that problem later.

Still, at the small angular scales, the polarisation data can be trusted and in this data Planck have one of their most impressive figures. The figure below shows how both the temperature multiplied by the polarisation (pixel by pixel on the sky) and how the polarisation itself varies with angular scale. The blue dots are the measured signal. Now, the red curve is not the best fit curve to this data. That is worth pausing and reflecting on. If it isn't the best fit curve, then what is it?

These curves reflect some of the best of humanity. These are the tiny fluctuations in the polarisation of a field of radiation, left over from a hydrogen plasma that permeated the entire universe, 14 billion years ago. The oscillations in the curves come from sound waves in this hydrogen plasma. The curve is our prediction for this data, with no free parameters to play with at all. Just reflect on that. I'm unable to describe how incredible this is. We don't even know whether Shakespeare wrote Shakespeare's plays, but we can predict exactly what the polarisation in the CMB should look like.

That curve is the unique prediction from analysing Planck's temperature data. There are no free parameters in defining those red lines. Once the temperature data is analysed, we can make an unchangeable prediction for what the polarisation should look like. The fact that the red line goes straight through the blue data points is absolutely remarkable. However, if one believes in the big bang and standard cosmological model, this is all that could have happened. If one doesn't believe in the big bang, then not only is there no reason to suspect that the CMB exists, or that it is polarised, but certainly not that the way the polarisation averages on particular angular scales should look like that.

I think it is worth pausing for one second longer on this. I'm about to start describing a few "features" and anomalies that might be present in the Planck data. It is tempting for a person cynical about natural science to pick up on these anomalies and say "scientists don't understand what they're doing, look at all these anomalies". The thing is, scientists are trying to understand everything. It isn't enough that the model explains almost everything, every possible failure is looked for and analysed. If someone wants to replace the big bang, or any other aspect of cosmology (or well-established science) it isn't enough just to explain how to create these anomalies. Any alternative model must also reproduce everything that works. Without the big bang the prediction for that red line would be a horizontal line through zero. That wouldn't be called an anomaly, that would be called a completely failed model.

Tentative feature evidence

There are "features" in these curves. A feature is a collection of data points that are consistently above or below the red curves, over an extended range. Can you find them?

Look at the curves in the bottom panel of the figure above. These curves show the difference between the measured value of how the CMB temperature depends on angular scale and the best fit model from cosmology. Clearly some of the data points lie above the curve and some below. These data points have errors on them. We can't measure them perfectly, so this is what we expect. However, if there was a true "feature"in the data, something genuinely unlikely, then what would happen is that, over some range of \( l\) values the data points would lie either above or below the theoretical curve.

Planck claim to have found two of these features in the figure above. Before reading my next paragraph, have a look at that figure and see if you can find where these features should be. There are meant to be two, and only two (remember you're looking for a collection of data points next to each other that consistently lie above or below the theoretical line)...

Found them? Well, when Planck analyses the data, allowing for isolated features to exist in the primordial signal, they find two regions where a feature can improve the fit to the data. One is at very large angular scales (at \(l\simeq 20\)) and one is at very small angular scales (at \(l\simeq 1700\)). I think if you look carefully you can see these two features in the curve above (at least I can convince myself that the blue data points are consistently below the theoretical curve). Now, neither of these features are all that statistically significant, but introducing them does help fit the data.

There are a variety of possible models for how such features can arise but all of them require adding additional parameters to the standard cosmological model.

This would be a pretty bleak situation (i.e. the features may be real, but they may not, we'll never know) if it weren't for one thing. All of these models that would predict features in the temperature, also predict features in the polarisation. Great, you might think, let's just look at the polarisation.

Problem.

As I wrote above, one of these features is at a very large angular scale and one at a very small angular scale. I've already mentioned Planck's problems with the large angular scales. Hopefully one day they'll get this sorted (they seem confident) and we'll be able to see. Unfortunately, Planck's excellent resolution in measuring the temperature is not quite as excellent with the polarisation. And, this particular small angle feature is at angles too small for Planck to resolve in the polarisation. This doesn't make this feature untestable ever, it just means we'll need to wait for a new telescope to make these measurements.

Bispectra

All of the curves above are called power spectra. What they essentially do is tell you how the CMB's temperature or polarisation will look if you average it over two points separated by a particular angle. If the power spectrum has a larger amplitude at a particular angle, then the CMB's temperature should look more similar over those angles (i.e. if it is hotter at one point, then it should also be hotter at another point that is that particular angle away from it). If the amplitude is smaller at a particular angle, then the CMB will look less similar over those angles.

Why stick to two points though? If one can calculate an average over sets of two points on the sky one can also calculate an average over sets of three points on the sky. This is called a bispectrum. One of Planck's biggest drawcards was its ability to constrain the bispectrum of the CMB's temperature anisotropies.

And it did.

In the standard cosmological model, the primordial bispectrum should be almost zero. It should be so close to zero that no experiment yet conceived should be able to detect it. This is because the standard cosmological model predicts that the primordial density perturbations should have a Gaussian distribution and a Gaussian distribution has a zero bispectrum. You might have heard about the search for "non-Gaussianities". This is it. This is what we've been obsessing about when we talk about non-Gaussianity because the primary way in which Planck searched for non-Gaussianities was by searching for a non-zero bispectrum.

There were high hopes. WMAP, Planck's predecessor, had seen tentative evidence for a non-zero bispectrum in a number of different ways. It was known that Planck would reduce the uncertainties on the bispectrum and the hope (maybe even the expectation) was that Planck would detect it with high significance.

This just didn't happen.

Instead, Planck has constrained the bispectrum quite tightly. Each of the ways in which WMAP was seeing evidence for a bispectrum, Planck has shown it to favour zero. Of course, a two-point average depends on just one number, the angular separation of the points. However, a three-point average will also depend on how the three points are oriented with respect to each other. Therefore, there are many ways in which a bispectrum can be non-zero and Planck has only analysed some of them.

Moreover, Planck does find tentative evidence for bispectrum features. What this means is that if they search for a non-zero bispectrum that is highly localised in terms of the angular separation of the three points they see some hints of a non-zero signal. This is similar to the features in the power-spectrum I described above. This is interesting, but perhaps not compelling. The reason it isn't compelling is that they analysed a lot of possible bispectrum features. Most of these features were consistent with zero and a few weren't. If you look for a signal in enough hay-stacks eventually you will find one.

A "feature" bispectrum. See how it depends on three different angular scales? See how it is localised to one particular set of these scales (i.e. it goes white when \(l\) gets big). Just as I told you. Other than that, this figure is going to have to be just eye candy. It's after midnight and I need to go to bed. Ask if you want more details.

But wait, there are features in both the power spectrum and the bispectrum, could they be related? good question. The simple answer is definitely, yes. Any model that generates a feature in one will almost definitely generate a feature in the other. However, both features should occur at the same angular scale. Here, they don't (or at least don't appear to - I'd love to be corrected if that was wrong!).

Trispectra

Well, if you can average over three-points, why not average over four? The number people use to quantify the amplitude of the bispectrum is parameterised as \(f_\mathrm{NL}\). This is the number Planck has found to favour zero. A four-point average, or trispectrum, would be parameterised by \(g_\mathrm{NL}\). Did Planck constrain \(g_\mathrm{NL}\)?

Not yet.

I've actually done some work on \(g_\mathrm{NL}\), so I was eagerly searching through Planck's non-Gaussianity paper in March looking for these constraints, only to find nothing. \(g_\mathrm{NL}\) is interesting because it would enhance the abundance of extreme over-densities in the universe and extreme under-densities at the same time. \(f_\mathrm{NL}\) can only do one or the other, but not both. This could make \(g_\mathrm{NL}\) a candidate explanation for the ISW mystery, which I've blogged extensively about.

I overheard today that the reason why no \(g_\mathrm{NL}\) constraints were announced in March is the same reason for no use of polarisation data to do cosmology. That is, the \(g_\mathrm{NL}\) analyses are failing "null tests". What this means, is that when the CMB maps are analysed in a way such that the result for \(g_\mathrm{NL}\) should be zero, it still gives a non-zero signal. An example of this is when the maps generated from intensity measurements at two different frequencies are subtracted from each other. The CMB should cancel, and thus the four-point average should be zero. If it isn't, something is going wrong. This problem is less of an issue for the bispectrum (although not completely non-existent).

Tension between CMB and astrophysics

The tension between astrophysical measurements of some cosmological parameters and the measurements of those parameters by Planck was mentioned early today. This is one of the most fascinating things to come out of Planck.

The primary two tensions here are measurements of the expansion rate of the universe and measurements of the abundance of galaxy clusters.

It is tempting to dismiss these tensions as systematic errors being made on the astrophysics side. The justification for this relates to what I wrote in my first post about Planck; it is very easy to predict what we should see in the CMB, but much more difficult for other cosmological probes. However, these other measurements are the most honest estimates, using what we know about astrophysics, to constrain these parameters. We shouldn't be so hasty to dismiss all of astrophysics so readily. What if this is due to new physical effects instead?

This is the main topic of the talks tomorrow, but I'll leave you with an image showing, quite strikingly, that this discrepancy really does exist. It is the constraints obtained on the amplitude of primordial density perturbations on a given distance scale plotted against the constraints on the density of matter in the universe. The blue curves come from the abundance of galaxy clusters (detected by Planck) and the red curves come from Planck's CMB measurements.

Now that is what I call a feature in the Planck data. The blue curves are what Planck's clusters tell us about cosmology. The red curves, what Planck's CMB measurements tell us. The way to interpret curves like this is that the preferred value of the parameter is the one inside the curves. I think I can see this feature by eye.

Something is clearly going on...

(Feedback and questions are welcome. was this too technical, not technical enough? Do you want more figures or less figures? Would you like me to quote actual numbers for the parameters I mention, or are you happy with descriptions?)

1) You should take a look at my post about the second day's talks as I go into this in a bit more detail. But the answer is that this would make the cluster based estimates of the matter density and amplitude of primordial density perturbations increase. This would bring the clusters in line with the CMB measurements. (Curiously, as I explained in yesterday's post, if Planck were just over-estimating the errors on their mass measurements then this could also be causing the discrepancy)

2) Well, Planck isn't discrepant with *all* other cosmological measurements. It matches with WMAP and with Baryon Acoustic Oscillation measurements relatively well. That Planck and WMAP match suggests that the CMB is being measured well. Also, note that the CMB is easier to predict in models than late-universe things are. It will be very expensive to build another telescope to verify Planck's full sky measurements (though note that both ACT and SPT are measuring the same signal on smaller patches of the sky - ACT is consistent with Planck, but SPT is slightly discrepant; however I just heard a very interesting rumour about that, which I will be writing up soon). A final point I would make is that the cosmological measurements that *were* discrepant already seem to be converging on Planck's new results. We had a talk here yesterday about supernovae measurements of the expansion rate and it appears that (independently) they were already going to revise their measurements towards a lower value (which will be more in line with Planck).

I hope that helps... do stay tuned though for the interesting stuff about Planck and SPT (I'm quite excited by what I overheard)!

All of the curves above are called power spectra. What they essentially do is tell you how the CMB's temperature or polarisation will look if you average it over two points separated by a particular angle. If the power spectrum has a larger amplitude at a particular angle, then the CMB's temperature should look more similar over those angles (i.e. if it is hotter at one point, then it should also be hotter at another point that is that particular angle away from it). If the amplitude is smaller at a particular angle, then the CMB will look less similar over those angles.

- Well, this is a short description, but I'm curious about the more technical details how this power spectrum is computed. I already know that the power spectrum is the Fourier transform of the 2-point correlation function, and that the measured angle on the sky is related to the multipole moment l and the wavenumber k.

- The vertical axis of the last diagram is labeled sigma-8. I think this is not correct: the sigma-8 value can not be as large as about 0.86. The Planck paper XVI gives the best fit value of 0.8288. So the vertical axis should be labeled as in the second diagram of your post "Day Two" to make both figures consistent..

I'm a little confused about your first question. You seem to be asking me for more technical detail about how the *power* spectrum is calculated, but you also seem to know all the technical details. If you want the absolute nitty gritty relating to issues of blocking out the galaxy and questions of numerical algorithms Planck use then I'm afraid I just don't know the details. Were you interested in the technical details for the *bi*spectrum? If so, then the bispectrum is simply the Fourier transform of the three-point correlation function. Sorry if that didn't help. Please feel free to ask the question again if it didn't.

- Regarding the vertical axis in the last figure, I took that straight from Planck's paper XX, so if there is a mistake it is also theirs. Your comments seem reasonable though, those Planck contours do seem quite high. I'll keep it in mind and try to ask someone the next chance I get, but that might not be for a few months at least.

I'd like to refer to my last post. In the meantime I had a look at the Planck papers XX and XVI. From Fig.10 of XX it is easy to calculate a sigma-8 = 0.821 with the Omega-M value = 0.315 given in Planck's CMB paper XVI (Tables 2 and 5). These tables also indicate a sigma-8 value of about 0.83 which is LESS than the average sigma-value shown in Fig.11 of paper XX (about 0.86).Therefore, reporting this lower sigma value in Fig.11 of XX the likelihood contours of cluster-SZ and CMB will begin to intersect. And - who knows - maybe after some corrections in cluster modeling, intersection would occur, and then, instead of saying "ignore clusters at your peril" one could say "include clusters for your profit"!